Stars close to the Eddington luminosity can have large low-density inflated envelopes. We show that the rise times of shock breakout signals from supernovae can be extended significantly if supernova progenitors have an inflated stellar envelope. If the shock breakout occurs in inflated envelopes, the shock breakout signals diffuse in them, and their rise time can be significantly extended. Then, the rise times of the shock breakout signals are dominated by the diffusion time in the inflated envelope rather than the light-crossing time of the progenitors. We show that our inflated Wolf-Rayet star models whose radii are on the order of the solar radius can have shock breakout signals that are longer than ~100 s. The existence of inflated envelopes in Wolf-Rayet supernova progenitors may be related to the mysterious long shock breakout signal observed in Type Ib SN 2008D. Extended shock breakout signals may provide evidence for the existence of inflated stellar envelopes and can be used to constrain the physical properties of these enigmatic structures.

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